Size and Degree Anti-Ramsey Numbers

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A copy of a graph H in an edge colored graph G is called rainbow if all edges of H have distinct colors. The size anti-Ramsey number of H, denoted by ARs(H), is the smallest number of edges in a graph G such that any of its proper edge-colorings contains a rainbow copy of H. We show that ARs(Kk)=Θ(k6/log2k). This settles a problem of Axenovich, Knauer, Stumpp and Ueckerdt. The proof is probabilistic and suggests the investigation of a related notion, which we call the degree anti-Ramsey number of a graph.

Original languageEnglish (US)
Pages (from-to)1833-1839
Number of pages7
JournalGraphs and Combinatorics
Issue number6
StatePublished - Jun 3 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


  • Anti-Ramsey
  • Proper edge coloring
  • Rainbow subgraph


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